As presented at Penn State on 2021-03-12HEADv1.0master

7 files changed, 355 insertions, 0 deletions

diff --git a/figs/energy.fig/Makefile b/figs/energy.fig/Makefile
new file mode 100644
index 0000000..e8d3f12
--- /dev/null
+++ b/figs/energy.fig/Makefile
@@ -0,0 +1,28 @@
+PROJECTNAME=erho_effective erho_fulleq erho_lowhigh
+
+PDFS=$(addsuffix .pdf, $(PROJECTNAME))
+
+all: $(PDFS)
+
+$(PDFS):
+	gnuplot $(patsubst %.pdf, %.gnuplot, $@) > $(patsubst %.pdf, %.tex, $@) 
+	pdflatex -file-line-error $(patsubst %.pdf, %.tex, $@)
+
+install: $(PDFS)
+	cp $^ $(INSTALLDIR)/
+
+$(LIBS):
+	ln -fs libs/$@ ./
+
+clean-libs:
+	rm -f $(LIBS)
+
+clean-aux:
+	rm -f $(addsuffix .aux, $(PROJECTNAME))
+	rm -f $(addsuffix .log, $(PROJECTNAME))
+	rm -f $(addsuffix .tex, $(PROJECTNAME))
+
+clean-tex:
+	rm -f $(PDFS)
+
+clean: clean-libs clean-aux clean-tex
diff --git a/figs/energy.fig/erho.dat b/figs/energy.fig/erho.dat
new file mode 100644
index 0000000..837439f
--- /dev/null
+++ b/figs/energy.fig/erho.dat
@@ -0,0 +1,104 @@
+ # v(x)=exp(-|x|), order=100, tolerance=1e-14
+ #
+ # rho           energy
+ #
+ 1.00000000e-06  7.93445832e-06
+ 1.20226443e-06  9.54545091e-06
+ 1.44543977e-06  1.14842358e-05
+ 1.73780083e-06  1.38177301e-05
+ 2.08929613e-06  1.66265809e-05
+ 2.51188643e-06  2.00080034e-05
+ 3.01995172e-06  2.40792133e-05
+ 3.63078055e-06  2.89815779e-05
+ 4.36515832e-06  3.48856405e-05
+ 5.24807460e-06  4.19972045e-05
+ 6.30957344e-06  5.05647046e-05
+ 7.58577575e-06  6.08881446e-05
+ 9.12010839e-06  7.33299394e-05
+ 1.09647820e-05  8.83280780e-05
+ 1.31825674e-05  1.06412115e-04
+ 1.58489319e-05  1.28222614e-04
+ 1.90546072e-05  1.54534805e-04
+ 2.29086765e-05  1.86287394e-04
+ 2.75422870e-05  2.24617677e-04
+ 3.31131121e-05  2.70904370e-04
+ 3.98107171e-05  3.26819905e-04
+ 4.78630092e-05  3.94394317e-04
+ 5.75439937e-05  4.76093386e-04
+ 6.91830971e-05  5.74914264e-04
+ 8.31763771e-05  6.94502595e-04
+ 1.00000000e-04  8.39296065e-04
+ 1.20226443e-04  1.01470042e-03
+ 1.44543977e-04  1.22730542e-03
+ 1.73780083e-04  1.48514988e-03
+ 2.08929613e-04  1.79804690e-03
+ 2.51188643e-04  2.17798310e-03
+ 3.01995172e-04  2.63960836e-03
+ 3.63078055e-04  3.20083623e-03
+ 4.36515832e-04  3.88357954e-03
+ 5.24807460e-04  4.71465030e-03
+ 6.30957344e-04  5.72685888e-03
+ 7.58577575e-04  6.96035420e-03
+ 9.12010839e-04  8.46425370e-03
+ 1.09647820e-03  1.02986208e-02
+ 1.31825674e-03  1.25368572e-02
+ 1.58489319e-03  1.52685874e-02
+ 1.90546072e-03  1.86031268e-02
+ 2.29086765e-03  2.26736380e-02
+ 2.75422870e-03  2.76420977e-02
+ 3.31131121e-03  3.37052167e-02
+ 3.98107171e-03  4.11014850e-02
+ 4.78630092e-03  5.01195435e-02
+ 5.75439937e-03  6.11081308e-02
+ 6.91830971e-03  7.44879092e-02
+ 8.31763771e-03  9.07655413e-02
+ 1.00000000e-02  1.10550483e-01
+ 1.20226443e-02  1.34575061e-01
+ 1.44543977e-02  1.63718539e-01
+ 1.73780083e-02  1.99036030e-01
+ 2.08929613e-02  2.41793284e-01
+ 2.51188643e-02  2.93508614e-01
+ 3.01995172e-02  3.56003446e-01
+ 3.63078055e-02  4.31463277e-01
+ 4.36515832e-02  5.22511186e-01
+ 5.24807460e-02  6.32296416e-01
+ 6.30957344e-02  7.64601077e-01
+ 7.58577575e-02  9.23968602e-01
+ 9.12010839e-02  1.11585830e+00
+ 1.09647820e-01  1.34683126e+00
+ 1.31825674e-01  1.62477387e+00
+ 1.58489319e-01  1.95916654e+00
+ 1.90546072e-01  2.36140673e+00
+ 2.29086765e-01  2.84519724e+00
+ 2.75422870e-01  3.42701297e+00
+ 3.31131121e-01  4.12666196e+00
+ 3.98107171e-01  4.96795983e+00
+ 4.78630092e-01  5.97954056e+00
+ 5.75439937e-01  7.19583118e+00
+ 6.91830971e-01  8.65822353e+00
+ 8.31763771e-01  1.04164830e+01
+ 1.00000000e+00  1.25304420e+01
+ 1.20226443e+00  1.50720365e+01
+ 1.44543977e+00  1.81277534e+01
+ 1.73780083e+00  2.18015742e+01
+ 2.08929613e+00  2.62185132e+01
+ 2.51188643e+00  3.15288712e+01
+ 3.01995172e+00  3.79133506e+01
+ 3.63078055e+00  4.55892039e+01
+ 4.36515832e+00  5.48176270e+01
+ 5.24807460e+00  6.59126465e+01
+ 6.30957344e+00  7.92518063e+01
+ 7.58577575e+00  9.52890139e+01
+ 9.12010839e+00  1.14569987e+02
+ 1.09647820e+01  1.37750822e+02
+ 1.31825674e+01  1.65620322e+02
+ 1.58489319e+01  1.99126836e+02
+ 1.90546072e+01  2.39410530e+02
+ 2.29086765e+01  2.87842186e+02
+ 2.75422870e+01  3.46069846e+02
+ 3.31131121e+01  4.16074894e+02
+ 3.98107171e+01  5.00239474e+02
+ 4.78630092e+01  6.01427558e+02
+ 5.75439937e+01  7.23082394e+02
+ 6.91830971e+01  8.69343678e+02
+ 8.31763771e+01  1.04518842e+03
diff --git a/figs/energy.fig/erho_effective.gnuplot b/figs/energy.fig/erho_effective.gnuplot
new file mode 100644
index 0000000..f26252e
--- /dev/null
+++ b/figs/energy.fig/erho_effective.gnuplot
@@ -0,0 +1,38 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520"
+set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32"
+
+plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\
+ 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "."
diff --git a/figs/energy.fig/erho_fulleq.dat b/figs/energy.fig/erho_fulleq.dat
new file mode 100644
index 0000000..351d1b9
--- /dev/null
+++ b/figs/energy.fig/erho_fulleq.dat
@@ -0,0 +1,100 @@
+ 1.000000000000000e-06  7.943042518656766e-06 0
+ 1.202264434617413e-06  9.550219866068997e-06 0
+ 1.445439770745928e-06  1.148608224097378e-05 1
+ 1.737800828749376e-06  1.381647407426905e-05 1
+ 2.089296130854041e-06  1.662160583174429e-05 0
+ 2.511886431509582e-06  2.000065135391551e-05 0
+ 3.019951720402019e-06  2.406839054942614e-05 0
+ 3.630780547701017e-06  2.896662133595565e-05 1
+ 4.365158322401657e-06  3.486570260772683e-05 1
+ 5.248074602497723e-06  4.197087478032896e-05 1
+ 6.309573444801930e-06  5.052956242205629e-05 1
+ 7.585775750291836e-06  6.084048678334965e-05 1
+ 9.120108393559096e-06  7.326450648917462e-05 1
+ 1.096478196143185e-05  8.823760552067889e-05 1
+ 1.318256738556407e-05  1.062866339996179e-04 1
+ 1.584893192461114e-05  1.280484412743087e-04 1
+ 1.905460717963248e-05  1.542931396948374e-04 1
+ 2.290867652767775e-05  1.859523935537466e-04 1
+ 2.754228703338163e-05  2.241538298379074e-04 1
+ 3.311311214825908e-05  2.702629184292266e-04 1
+ 3.981071705534969e-05  3.259339774051344e-04 1
+ 4.786300923226380e-05  3.931723354869787e-04 1
+ 5.754399373371566e-05  4.744101435386617e-04 1
+ 6.918309709189363e-05  5.725988899895806e-04 1
+ 8.317637711026709e-05  6.913223659756494e-04 1
+ 1.000000000000000e-04  8.349346745163116e-04 1
+ 1.202264434617413e-04  1.008728918608530e-03 1
+ 1.445439770745928e-04  1.219143475424315e-03 1
+ 1.737800828749376e-04  1.474014314386416e-03 1
+ 2.089296130854039e-04  1.782883700975914e-03 1
+ 2.511886431509580e-04  2.157377911005317e-03 1
+ 3.019951720402016e-04  2.611669336976909e-03 1
+ 3.630780547701014e-04  3.163041683927843e-03 1
+ 4.365158322401661e-04  3.832580921405091e-03 1
+ 5.248074602497728e-04  4.646019387820095e-03 1
+ 6.309573444801930e-04  5.634766055532872e-03 1
+ 7.585775750291835e-04  6.837162598523666e-03 1
+ 9.120108393559096e-04  8.300012713479526e-03 1
+ 1.096478196143185e-03  1.008044129788173e-02 1
+ 1.318256738556408e-03  1.224815077758103e-02 1
+ 1.584893192461114e-03  1.488815434797412e-02 1
+ 1.905460717963246e-03  1.810408049926405e-02 1
+ 2.290867652767772e-03  2.202216044849479e-02 1
+ 2.754228703338166e-03  2.679603069994577e-02 1
+ 3.311311214825911e-03  3.261250778551406e-02 1
+ 3.981071705534973e-03  3.969852233927642e-02 1
+ 4.786300923226385e-03  4.832943621884326e-02 1
+ 5.754399373371567e-03  5.883901075761193e-02 1
+ 6.918309709189363e-03  7.163134806415740e-02 1
+ 8.317637711026709e-03  8.719519272244317e-02 1
+ 1.000000000000000e-02  1.061210611088454e-01 1
+ 1.202264434617413e-02  1.291217632376783e-01 1
+ 1.445439770745928e-02  1.570570011615084e-01 1
+ 1.737800828749376e-02  1.909628719282619e-01 1
+ 2.089296130854041e-02  2.320872756251715e-01 1
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+ 3.630780547701010e-02  4.153823512868898e-01 1
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+ 7.585775750291836e-02  8.956203622431048e-01 1
+ 9.120108393559097e-02  1.083759966304908e+00 1
+ 1.096478196143185e-01  1.310719973979596e+00 1
+ 1.318256738556407e-01  1.584396355238566e+00 1
+ 1.584893192461114e-01  1.914280945866737e+00 1
+ 1.905460717963248e-01  2.311784046064119e+00 1
+ 2.290867652767775e-01  2.790622317703228e+00 1
+ 2.754228703338169e-01  3.367285183378040e+00 1
+ 3.311311214825908e-01  4.061595587917465e+00 1
+ 3.981071705534969e-01  4.897384186423424e+00 1
+ 4.786300923226380e-01  5.903299886083452e+00 1
+ 5.754399373371566e-01  7.113784322007290e+00 1
+ 6.918309709189363e-01  8.570243441380599e+00 1
+ 8.317637711026709e-01  1.032245608693097e+01 1
+ 1.000000000000000e+00  1.243026753303222e+01 1
+ 1.202264434617413e+00  1.496562561057760e+01 1
+ 1.445439770745928e+00  1.801502869576436e+01 1
+ 1.737800828749376e+00  2.168246883802093e+01 1
+ 2.089296130854041e+00  2.609297014699965e+01 1
+ 2.511886431509582e+00  3.139684282320142e+01 1
+ 3.019951720402019e+00  3.777479758723231e+01 1
+ 3.630780547701010e+00  4.544409456028400e+01 1
+ 4.365158322401657e+00  5.466593586138625e+01 1
+ 5.248074602497723e+00  6.575435350738108e+01 1
+ 6.309573444801930e+00  7.908689506783082e+01 1
+ 7.585775750291836e+00  9.511747067219883e+01 1
+ 9.120108393559097e+00  1.143917984731058e+02 1
+ 1.096478196143185e+01  1.375659740282897e+02 1
+ 1.318256738556407e+01  1.654287952107530e+02 1
+ 1.584893192461114e+01  1.989286012247062e+02 1
+ 1.905460717963248e+01  2.392055363411829e+02 0
+ 2.290867652767775e+01  2.876303621855438e+02 0
+ 2.754228703338169e+01  3.458511552270688e+02 0
+ 3.311311214825908e+01  4.158492765508882e+02 0
+ 3.981071705534969e+01  5.000067330413117e+02 0
+ 4.786300923226381e+01  6.011878314695363e+02 0
+ 5.754399373371567e+01  7.228352310513908e+02 0
+ 6.918309709189363e+01  8.690894472935229e+02 0
+ 8.317637711026708e+01  1.044926046890143e+03 0
diff --git a/figs/energy.fig/erho_fulleq.gnuplot b/figs/energy.fig/erho_fulleq.gnuplot
new file mode 100644
index 0000000..2927ead
--- /dev/null
+++ b/figs/energy.fig/erho_fulleq.gnuplot
@@ -0,0 +1,37 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+plot "erho.dat" using 1:($2/$1) with lines linestyle 1 ,\
+ "erho_fulleq.dat" using 1:($2/$1) with lines linestyle 4 ,\
+ 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "." ,\
+ "holzmann_2019-12-25.dat" using 1:($2/$1) with points linestyle 2
diff --git a/figs/energy.fig/erho_lowhigh.gnuplot b/figs/energy.fig/erho_lowhigh.gnuplot
new file mode 100644
index 0000000..9d2a590
--- /dev/null
+++ b/figs/energy.fig/erho_lowhigh.gnuplot
@@ -0,0 +1,37 @@
+set ylabel "$\\displaystyle\\frac{e}{\\rho}$" norotate offset -1,0
+set xlabel "$\\rho$"
+
+set xtics 1e-6, 100, 100
+set xtics add ("$10^{-6}$" 0.000001, "$10^{-4}$" 0.0001, "$10^{-2}$" 0.01, "$1$" 1.0, "$10^2$" 100)
+unset mxtics
+
+set ytics 8,1
+set mytics 2
+
+set xrange [0.000001:100]
+set yrange [7.5:13.5]
+
+# default output canvas size: 12.5cm x 8.75cm
+set term lua tikz size 8,6 standalone
+
+set key off
+
+
+# set linestyle
+set style line 1 linetype rgbcolor "#4169E1" linewidth 3
+set style line 2 linetype rgbcolor "#DC143C" linewidth 3
+set style line 3 linetype rgbcolor "#32CD32" linewidth 3
+set style line 4 linetype rgbcolor "#4B0082" linewidth 3
+set style line 5 linetype rgbcolor "#DAA520" linewidth 3
+
+set pointsize 1
+
+set logscale x
+
+a=1.25435641059
+
+set label at 0.0001,2*pi*a*1.03 "LHY" textcolor "#DAA520"
+set label at 0.1,4.1*pi "Hartree" textcolor "#32CD32"
+
+plot 2*pi*a*(1+128/15/sqrt(pi)*sqrt(x*a**3)) linestyle 5 dashtype "." ,\
+ 4*pi linestyle 3 dashtype "."
diff --git a/figs/energy.fig/holzmann_2019-12-25.dat b/figs/energy.fig/holzmann_2019-12-25.dat
new file mode 100644
index 0000000..96689cb
--- /dev/null
+++ b/figs/energy.fig/holzmann_2019-12-25.dat
@@ -0,0 +1,11 @@
+## data from M. Holzmann, 2019-09-22
+# rho          E0    n0
+1e-6     7.902e-6
+1e-4    8.3441e-4  0.0171
+1e-3   9.13384e-3  0.0481
+1e-2  1.061073e-1  0.0871
+1e-1   1.19182e+0  0.0851
+1e-0   1.24302e+1  0.0587
+1e+1   1.25442e+2  0.0319
+5e+1   6.28032e+2   0.021
+